Twilio evangelist here.
The parameters get converted into form encoded values and included in the HTTP request that is made to the URL configured for your TwiML App.
So for example, if you include parameters like this:
params = {"PhoneNumber": "+15555555555"};
Twilio.Device.connect(params);
they will get converted into this set of form encoded values and included in the POST request Twilio makes to your Twiml Apps Voice URL:
PhoneNumber=+15555555555
You can use whatever mechanism in your server side framework that exposes form values to grab those parameters and use them to generate and return TwiML. For example, in PHP:
$phoneNumber = $_REQUEST["PhoneNumber"];
Hope that helps.